[Todos] [Kolmogorov] Seminario de Probabilidad y Estadística Matemática

[Matthieu Jonckheere]

Seminario de Probabilidad y Estadística Matemática.

PRIMER ENCUENTRO 2013: Miércoles 23 de Enero, 12:00hs.

EXPOSITOR: Pietro Caputo, Universidad de Roma 3.
TITULO: LUGAR: Departamento de Matemática, Aula de seminarios, 2do
piso, Pabellón 1.

RESUMEN: We consider the (2+1)-dimensional SOS interface pinned at the
boundary of a lattice box in the low temperature phase. In the
presence of a positivity (hard wall) constraint, the interface is
pushed away from the wall at a height H=H(L) proportional to log(L),
where L is the side of the box. We give sharp estimates which quantify
this phenomenon, known as entropic repulsion, and show that the
ensemble of level lines of heights H,H-1,...has a macroscopic limit as
L diverges. The scaling limit is given by nested loops formed via
translates of Wulff shapes. Moreover, we analyze the effect of
entropic repulsion on the dynamics of the interface. We show that
relaxation to equilibrium occurs  through a sequence of metastable
transitions between successive layers until the final height H(L) is
achieved.   Our analysis shows that the spectral gap is exponentially
small in the parameter L, in contrast with the free case (no wall
constraint), where one expects polynomial bounds to hold.
Joint work with E.Lubetzky, F.Martinelli, A.Sly and F.L.Toninelli


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